| Title:
|
The first Dirichlet eigenvalue of bicyclic graphs (English) |
| Author:
|
Zhang, Guang-Jun |
| Author:
|
Zhang, Xiao-Dong |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
62 |
| Issue:
|
2 |
| Year:
|
2012 |
| Pages:
|
441-451 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, we have investigated some properties of the first Dirichlet eigenvalue of a bicyclic graph with boundary condition. These results can be used to characterize the extremal bicyclic graphs with the smallest first Dirichlet eigenvalue among all the bicyclic graphs with a given graphic bicyclic degree sequence with minor conditions. Moreover, the extremal bicyclic graphs with the smallest first Dirichlet eigenvalue among all the bicycle graphs with fixed $k$ interior vertices of degree at least 3 are obtained. (English) |
| Keyword:
|
first Dirichlet eigenvalue |
| Keyword:
|
bicyclic graph |
| Keyword:
|
degree sequence |
| MSC:
|
05C35 |
| MSC:
|
05C50 |
| idZBL:
|
Zbl 1265.05429 |
| idMR:
|
MR2990185 |
| DOI:
|
10.1007/s10587-012-0038-1 |
| . |
| Date available:
|
2012-06-08T09:43:13Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/142837 |
| . |
| Reference:
|
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| Reference:
|
[2] Friedman, J.: Some geometric aspects of graphs and their eigenfunctions.Duke Math. J. 69 (1993), 487-525. Zbl 0785.05066, MR 1208809, 10.1215/S0012-7094-93-06921-9 |
| Reference:
|
[3] Leydold, J.: The geometry of regular trees with the Faber-Krahn property.Discrete Math. 245 (2002), 155-172. Zbl 0999.05016, MR 1887936, 10.1016/S0012-365X(01)00139-X |
| Reference:
|
[4] Pruss, A. R.: Discrete convolution-rearrangement inequalities and the Faber-Krahn inequality on regular trees.Duke Math. J. 91 (1998), 463-514. Zbl 0943.05056, MR 1604163, 10.1215/S0012-7094-98-09119-0 |
| Reference:
|
[5] Zhang, G. J., Zhang, J., Zhang, X. D.: Faber-Krahn Type Inequality for Unicyclic Graphs.Linear and Multilinear Algebra, DOI: 10.1080/03081087.2011.651722. 10.1080/03081087.2011.651722 |
| Reference:
|
[6] Zhang, X. D.: The Laplacian spectral radii of trees with degree sequences.Discrete Math. 308 (2008), 3143-3150. Zbl 1156.05038, MR 2423396, 10.1016/j.disc.2007.06.017 |
| Reference:
|
[7] Zhang, X. D.: The signless Laplacian spectral radius of graphs with given degree sequences.Discrete Appl. Math. 157 (2009), 2928-2937. Zbl 1213.05153, MR 2537494, 10.1016/j.dam.2009.02.022 |
| . |
